
where \(\hat{\tau }\)  is the estimate of the true \(\tau \) . Since there is a relationship between \(\tau \)  and \(\mathbf {p}_{\text{ris}}\) , the FIM of position and orientation \(\mathbf {J}\left( \zeta \right)\)  can be derived as \(\mathbf {J}\left( \zeta \right) = \mathbf {T}^\top \mathbf {J}\left( \eta \right) \mathbf {T}\) , where \(\mathbf {T}\in \mathbb {R}^{6\times 5}\)  is a Jacobian matrix [1]}. Its element on the \(\ell \) th row and the \(q\) th column is defined
\(\left[\mathbf {T}\right]_{\ell ,q} = \frac{\partial \left[\eta \right]_{\ell }}{\partial \left[\zeta \right]_{q}} \quad .\) 
